Maths in Year 5: what Lärkompis practises
In Year 5 of Swedish school (around age 11), Lärkompis practises 39 skills in maths, linked to 25 of 27 items in the core content of Lgr22, the Swedish national curriculum, for Years 4–6. The areas are algebra; geometry; problem solving; relationships and change; probability and statistics; and understanding and using numbers. Each skill has five difficulty levels, and the skills are practised in 12 mini-games, including Rätta roboten (Fix the Robot), Kunskapsjakten (Knowledge Hunt) and Bråkpizzan (Fraction Pizza).
Lgr22 sets out core content for each stage (Years 4–6), not for each year. So Lärkompis spreads the skills across the years using its own time windows, and these are estimates. For Year 5, this means that 17 skills start this year and 22 skills started earlier and are still being practised. The figure 25 of 27 counts the items in the core content from Skolverket (the Swedish National Agency for Education) that at least one skill links to; it does not mean the whole item is covered.
What Lärkompis practises in Year 5
The 39 skills in maths in Year 5 are grouped into 6 areas following Skolverket's syllabus. Under each skill you can see the first and the last difficulty level, so you know how far the exercises go.
Algebra
- The equals sign and solving simple equations Level 1: x + 7 = 15. Level 5: 2x − 5 = 11.
- Patterns in number sequences and geometric patterns (already starts in Year 4) Level 1: The next number in an increasing sequence. Level 5: Choose the rule: 3 · n + 2.
- Programming in visual environments, and algorithms (already starts in Year 4) Level 1: Three to four cards on a grid. Level 5: Repeat and if-obstacle cards, the shortest possible program.
- Variables in simple algebraic expressions Level 1: The value of x + 5 when x = 6. Level 5: Expressions with brackets, situations with several steps.
Geometry
- Area of rectangles, triangles and compound shapes (already starts in Year 4) Level 1: Rectangle in cm². Level 5: Triangle with base and height, or a missing side from the area.
- Converting units of length, mass, volume and time Level 1: m, dm, cm and mm in whole numbers. Level 5: Two decimal places: 2.39 kg = 2390 g.
- Perimeter of rectangles, triangles and compound shapes (already starts in Year 4) Level 1: Rectangle with given sides. Level 5: Corner cut out: the perimeter stays the same.
- Scale in reductions and enlargements Level 1: Drawing at a scale of 1:2, 1:5 or 1:10 to real life. Level 5: Map at a scale of 1:10,000, converting to metres.
- Lines of symmetry and reflection (already starts in Year 4) Level 1: Lines of symmetry in letters. Level 5: Reflect a corner of a shape.
- Types of angle and angle sums Level 1: Acute, right or obtuse angle. Level 5: Angles around a point (360°).
Problem solving
- Solving problems with logical reasoning and a table (already starts in Year 4) Level 1: Three people: clues with “not” and “has”. Level 5: All kinds of clue, where the answer depends on several clues together.
Relationships and change
- The same proportion as a fraction, a decimal and a percentage Level 1: Fractions to percentages: 1/2, 1/4, 3/4. Level 5: Hundredths and twentieths.
- Graphs that show proportional relationships Level 1: Read the price from a graph with points. Level 5: Read a graph with a starting fee.
- Coordinate grids and the scales on the axes Level 1: Go to a point from the origin. Level 5: The fourth corner of the rectangle.
- Percentages of an amount, discounts and proportions as percentages Level 1: 50%, 25% and 10% of round numbers. Level 5: What percentage of 20 is 15.
- Proportionality, unit prices and everyday problem solving Level 1: The price of one when several cost a certain amount. Level 5: A recipe for more buns.
Probability and statistics
- Simple combinations in real-life situations Level 1: Two choices: tops and trousers. Level 5: Putting three or four people in a queue.
- Averages (mean, median and mode) and range Level 1: Mode. Level 5: The median of an even number of values, a missing value from the mean.
- Probability in simple chance experiments, and comparing experiments Level 1: Which colour is most likely. Level 5: Compare two bags with different numbers of marbles.
- Reading and interpreting tables and bar charts (already starts in Year 4) Level 1: The largest value in a small table. Level 5: The mean from a table with five categories.
Understanding and using numbers
- Rounding whole numbers and decimals (already starts in Year 4) Level 1: Numbers under 100 to the nearest ten (with a number line); decimals with one decimal place to the nearest whole number. Level 5: Mixed, where rounding crosses a boundary (3,996 → 4,000, 0.998 → 1), and choosing the unit.
- Adding and subtracting fractions Level 1: Same denominator, 1/4 + 2/4. Level 5: Different denominators with no simple link: 2/3 + 1/5.
- Mixed numbers and improper fractions Level 1: How many wholes are 6 halves. Level 5: Converting both ways and choosing the right number: 21/4.
- Fractions of a quantity (already starts in Year 4) Level 1: 1/2 of 4. Level 5: Word problems and the whole amount: 2/3 of Nils’s cards is 14, how many does Nils have.
- Equivalent fractions and simplifying Level 1: Expanding: 1/2 = 2/□. Level 5: Mixed: expanding, simplifying and spotting fractions that are equal.
- Comparing and ordering fractions (already starts in Year 4) Level 1: Same denominator: which of 3/4, 2/4 and 1/4 is smallest. Level 5: Ordering fractions, including ones greater than 1, and placing 6/4 on the number line.
- Adding and subtracting decimals Level 1: Tenths below 1: 0.3 + 0.4 and 0.9 − 0.4, with a number line. Level 5: Three numbers, thousandths and 10 − 3.85.
- Multiplying and dividing by 10, 100 and 1,000 Level 1: Times 10 with tenths: 3.4 · 10. Level 5: Mixed, with thousandths: 0.035 · 1,000 and 12.5 ÷ 1,000.
- Multiplying and dividing decimals by whole numbers Level 1: Tenths times 2–5 and divided by 2–4: 0.4 · 3 and 0.6 ÷ 2. Level 5: Two-digit numbers: 3.6 · 25 and 5.4 ÷ 12.
- Comparing and ordering decimals (already starts in Year 4) Level 1: Tenths (0.3, 0.7, 0.5): which is biggest, ordering four numbers, counting 0.8 – 0.9 – 1.0. Level 5: Numbers that start the same way (0.5, 0.45, 0.405, 0.54), descending order and counting in hundredths past whole numbers.
- Mental arithmetic with division (already starts in Year 4) Level 1: Division within the times tables: 42 ÷ 6. Level 5: Dividing by tens (480 ÷ 60) and the 11 and 12 times tables (144 ÷ 12).
- Written division (the bus stop method) (already starts in Year 4) Level 1: Two-digit by one-digit, no remainder: 96 ÷ 4. Level 5: Dividing by a two-digit number, no remainder: 504 ÷ 12.
- Mental arithmetic with multiplication (already starts in Year 4) Level 1: Tens times ones (30 · 4), and times 10 and 100. Level 5: Clever tricks: 11 · n, 99 · n, 15 · an even number and 25 · n.
- Multiplication using the column method (already starts in Year 4) Level 1: Two-digit times one-digit without carrying: 23 · 3. Level 5: Three-digit times two-digit: 253 · 34.
- The times tables 2–12 (knowing them by heart) (already starts in Year 4) Level 1: The 2, 3, 4, 5 and 10 times tables (revision) with pictures of rows and columns. Level 5: Times tables up to 12, and a missing factor.
- Money with öre (hundredths of a krona), change and price per kilo (decimals in everyday life) Level 1: Adding two prices in whole kronor and fifty öre; price times 2–4. Level 5: Several items with change, price per 100 g with half kilos, splitting the bill between several people.
- Order of operations: multiplication before addition, brackets first Level 1: Multiplication before addition: 2 + 3 · 4. Level 5: Longer expressions with brackets, and choosing where the brackets go.
- Place value and large numbers (up to millions) (already starts in Year 4) Level 1: Numbers up to 9,999: the value of a digit, comparing, one, ten or a hundred more. Level 5: Mixed: whole thousands, ten, a hundred and a thousand times as big, a hundred thousand and a million more or less.
- Rough estimates and checking whether answers are reasonable (already starts in Year 4) Level 1: Rough estimate with tens: 38 + 52 ≈ 40 + 50; a reasonable answer in addition and subtraction. Level 5: Four- and five-digit numbers, division and everyday problems where the answer should be reasonable.
What the syllabus says, in short
The Lgr22 core content for Years 4–6 in maths, summarised in our own words for the parts Lärkompis practises in Year 5. Read the full text in Skolverket's English translation of Lgr22.
- Rational numbers, which means negative numbers, fractions and decimals too, and how they are connected.
- Percentages and how they relate to fractions and decimals.
- Methods for calculating in your head, with rough estimates and on paper, including with simple fractions and decimals. Checking answers: is the answer reasonable?
- Equality, simple equations, variables and how to solve simple equations.
- Perimeter, area, angles, converting between units, and scale.
- Mean, mode and median, tables and charts, and simple combinatorics (counting possible combinations).
- Proportionality, coordinate systems and graphs.
- Programming in visual programming environments, and solving problems using different strategies.
How to help at home with maths in Year 5
Year 5 is the middle of the middle stage. It pays to revise what was secure in Year 4 before new things are added on top, and to deal with small gaps while they are still small. Ask “how did you work it out?” more often than “what did you get?”, and use the same models and written methods as the teacher, so your child does not have two different methods to keep track of.
- Double or halve the recipe. Cook something where you make a double or half batch. Let your child work out the fractions and decimals (3/4 dl, where a decilitre is 100 ml, becomes how much?). Ask whether the answer is reasonable before you pour it in. Works in everyday life: about 15 minutes.
- Card games with fractions and numbers. Play with an ordinary pack of cards: draw two cards and make a number from them (tens and ones); the biggest number wins. Vary it: draw three cards, or work out the difference. The game practises place value without feeling like homework. As a game: about 10 minutes.
- Sale prices in a shop. Look at a price tag with 25% off. Ask: roughly how much cheaper is it, and what does it cost now? Explain why 25% is a quarter. Let your child estimate before reaching for the calculator. Works in everyday life: about 10 minutes.
- Ask your child to teach you. Say: “I don’t know this particular method. Can you show me how you do it at school?” Explaining forces understanding, and you avoid teaching a different method from the school’s. Ask questions instead of giving answers. When it is hard going: about 10 minutes.
How you can tell it has clicked in Year 5
- Proportionality, unit prices and everyday problem solving: Your child first works out what one costs.
- Simple combinations in real-life situations: Your child draws a tree diagram or makes a systematic list.
- Averages (mean, median and mode) and range: Your child sorts the numbers before looking for the median.
- Probability in simple chance experiments, and comparing experiments: Your child compares proportions, not just numbers.
Common pitfalls in Year 5
- Mixed numbers and improper fractions: Writes 5/3 as 1 5/3 or 2 1/3.
- Equivalent fractions and simplifying: Thinks 2/4 and 1/2 are different amounts.
- Adding and subtracting decimals: Forgets to carry from the tenths: 4.7 + 2.6 becomes 6.3.
- Multiplying and dividing by 10, 100 and 1,000: Just adds a zero: 3.4 · 10 becomes 3.40.
If maths practice in Year 5 often ends in tears or takes far too long, stop for the day and write a few lines to the teacher about what was hard. That is useful information for the school, not a failure.
Games that practise it
In Year 5 maths, Lärkompis uses 12 mini-games. In these games, playing is the practice, so your child learns while they play. There are no points or streaks, and no ads.
Rätta roboten (Fix the Robot)
Knut has made a mistake and your child teaches him the right way. Explaining the mistake is the skill. In Year 5, the game practises 16 skills: the equals sign and solving simple equations; variables in simple algebraic expressions; area of rectangles, triangles and compound shapes; perimeter of rectangles, triangles and compound shapes; and more.
Kunskapsjakten (Knowledge Hunt)
A quiz show in a TV studio, where Vera leads the questions up a ladder. There are lifelines but no points: the ladder fills up with the questions your child has worked through. In Year 5, the game practises 10 skills: converting units of length, mass, volume and time; scale in reductions and enlargements; lines of symmetry and reflection; types of angle and angle sums; and more.
Bråkpizzan (Fraction Pizza)
A pizza is cut into slices and the slices are the fractions: your child cuts, compares and adds them up. In Year 5, the game practises 6 skills: the same proportion as a fraction, a decimal and a percentage; adding and subtracting fractions; mixed numbers and improper fractions; fractions of a quantity; and more.
Butiken (The Shop)
Your child pays, gets change and compares prices with real coins. In Year 5, the game practises 6 skills: percentages of an amount, discounts and proportions as percentages; proportionality, unit prices and everyday problem solving; rounding whole numbers and decimals; comparing and ordering decimals; and more.
Flodhoppet (River Hop)
Pix hops across the river on stepping stones that sit on a number line. In Year 5, the game practises 4 skills: percentages of an amount, discounts and proportions as percentages; mixed numbers and improper fractions; comparing and ordering fractions; and adding and subtracting decimals.
Tidslinjen (The Timeline)
Your child puts cards on a line in the right order, for example events, steps or numbers. A card in the right place turns over and shows the answer. In Year 5, the game practises 3 skills: comparing and ordering fractions; comparing and ordering decimals; and place value and large numbers (up to millions).
Formpusslet (Shape Puzzle)
A shape puzzle where the pieces are the skill: from pictures made of simple shapes to areas and Pythagoras’ theorem. In Year 5, the game practises 2 skills: area of rectangles, triangles and compound shapes; and lines of symmetry and reflection.
Detektiven (The Detective)
A short logic case each round: your child reads the clues, fills in a grid with crosses and ticks, and points out the answer. In Year 5, the game practises 1 skill: solving problems with logical reasoning and a table.
Kodaren (The Coder)
Knut the robot wants to reach the star, and your child builds the program from big cards. In Year 5, the game practises 1 skill: programming in visual environments, and algorithms.
Mönstermakaren (The Pattern Maker)
Patterns roll along a conveyor belt and your child fills the gaps so the pattern works. In Year 5, the game practises 1 skill: patterns in number sequences and geometric patterns.
Sorteringsbandet (The Sorting Belt)
A calm conveyor belt of things that your child puts in the right box by following a rule. In Year 5, the game practises 1 skill: the times tables 2–12 (knowing them by heart).
Vågen (The Balance)
A balance scale where using the scale is the skill: your child makes both sides weigh the same, works out what a box weighs or solves an equation by doing the same thing to both sides. In Year 5, the game practises 1 skill: the equals sign and solving simple equations.
Questions about maths in Year 5
What does Lärkompis practise in maths in Year 5?
Lärkompis has 39 skills in maths in Year 5, for example “The equals sign and solving simple equations”; “Patterns in number sequences and geometric patterns”; “Programming in visual environments, and algorithms”; “Variables in simple algebraic expressions”; and “Area of rectangles, triangles and compound shapes”. Each skill has five levels. In “The equals sign and solving simple equations”, for example, level 1 is “x + 7 = 15” and level 5 is “2x − 5 = 11”. The app adjusts the level to how your child is doing.
What comes after Year 5 in maths?
In Year 6, Lärkompis practises 23 skills in maths, and new that year are “The equals sign and solving simple equations”; “Scale in reductions and enlargements”; and “Asking maths questions about everyday situations”. Most of it builds on what your child practised in Year 5.
Which mistakes are common in maths in Year 5?
Common mistakes that Lärkompis covers include “Writes 5/3 as 1 5/3 or 2 1/3” in “Mixed numbers and improper fractions” and “Thinks 2/4 and 1/2 are different amounts” in “Equivalent fractions and simplifying”. When an answer is wrong, the app shows how to think it through instead of just marking it wrong, and the parent panel shows what your child is practising right now.
Does Lärkompis follow Lgr22 in maths in Year 5?
Yes. Every exercise in maths in Year 5 is linked to an item in the Lgr22 core content for Years 4–6; 25 of 27 items in maths have at least one linked skill. Lärkompis is a complement at home and does not replace teaching.
How much does it cost to practise maths in Year 5 with Lärkompis?
Lärkompis costs SEK 49, once, for all subjects and every child in the family, with future updates included. You can try maths in Year 5 for free first, without an account.
More years and subjects
The same year in other subjects:
